Department of Mathematics
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Item A comparative study of ε-constraint, lp-metric, and weighted sum multi-objective optimization methods in a circular economy(Elsevier, 2024) Kulshrestha, Rakhee; Sangwan, Kuldip SinghApproximately 74.7 Mt (Million Metric Tonnes) of e-waste is expected to be produced in 2030, and laptop e-waste is one of the major constituents of this. The goal of this paper is to develop and optimize a mixed-integer linear programming (MILP) mathematical model for a laptop manufacturer in India, based on a framework that integrates secondary reuse concept associated with traditional circular economy waste avoidance strategies. The multi-objective solution techniques of ε-constraint, LP-metric, and weighted sum methods are used to optimize the circular economy model. The proposed model aids as a policy tool to decide the optimum number of inspection/collection centers, sales/distribution centers, disassembly centers, refurbishing centers, recycling centers, and their optimum locations and allocations. This study results suggest that reuse, secondary customer centers, refurbishing, and recycling of the laptops is not only economically beneficial to the organization but also environment friendly and helps to create more jobs in the rural economy.Item Modelling and simultaneous optimization of environmental, economic, and technological factors in machining(Springer, 2023-10) Sangwan, Kuldip Singh; Kulshrestha, RakheeIn the current era, manufacturing industries are facing multifaceted challenges related to increasing environmental awareness, decreasing economic gains, and technology obsolesce. These challenges become more apparent during the machining of difficult-to-machine materials due to high tool wear rates, high cutting forces, undesirable surface quality, high tool replacement costs, and a stagnating productivity. The developed approach aims at improving environmental, economic, and technological factors by optimizing four performance characteristics–energy demand, surface roughness, tool wear, and material removal rate during the milling of H13 tool steel by using an integrated artificial neural network and genetic algorithm. The proposed methodology provides Pareto solutions for minimum energy demand, surface roughness, & tool wear, and maximum material removal rate. The novelty of this work lies in generating Pareto fronts for analyzing conflicting responses, and determining preferred solutions without sacrificing environmental, technological, and economic considerations, simultaneously. The present work will be significant to practitioners in adopting better management strategies and simultaneously dealing with these challenges. The potential of the research lies in directly integrating the proposed optimization module with the machine tool system to serve as an online tool for machine tool process optimization.Item A multi-objective fuzzy mathematical model for circular economy with leasing as a strategy(Emerald, 2024-05) Kulshrestha, Rakhee; Sangwan, Kuldip SinghThis paper proposes multi-objective fuzzy mixed integer linear programming mathematical model considering multi-product, multi-echelon and multi-capacitated concepts of the circular economy. The three objectives of the proposed model, namely, economic, environmental and social are solved simultaneously using constraint approach to obtain balanced trade-off between the objective functions. The model is validated by solving a case study from the literature. The proposed model is made pragmatic for industrial application by considering multi-external suppliers multi-customer zones, multi-disassembly centers, multi-collection centers and multi-refurbishing centers and accounting for purchasing, processing, transportation, set-up costs and capacity constraints at the same time.Item Blockchain-enabled solution for transparency and waste minimization in pharmaceutical supply chains(Elsevier, 2025) Sangwan, Kuldip Singh; Kulshrestha, RakheeThe pharmaceutical supply chain is a complex network involving multiple stakeholders and processes, making it susceptible to various inefficiencies and challenges such as counterfeiting, drug expiry, and inefficient inventory management. These challenges may lead to compromised patient safety and financial losses. Blockchain technology is a promising solution to these problems. This study develops a blockchain-enabled mathematical model for pharmaceutical supply chains. A distributed ledger is used to acquire the real-time drug transaction status throughout the supply chain. The study uses real-time data gathered from the distributed ledgers across the supply chain, ensuring optimum inventory with the minimization of expired drugs and transportation costs. By leveraging the proposed model, stakeholders can eliminate counterfeiting, reduce drug expiry, and ultimately ensure the integrity and safety of pharmaceutical products throughout their lifecycle. This model also helps manufacturers in decision making for drug manufacturing based on real-time data. Novelty of the study lies in real-time tracing and managing the drugs across the supply chain.Item Overcoming the extended producer responsibility challenges of packaging material through integrated refurbishing and recycling(Springer, 2024-11) Sangwan, Kuldip Singh; Kulshrestha, RakheeThis paper proposes a model to integrate the refurbishing and recycling activities with the forward supply chain aiming to overcome the recent challenges faced by the organizations while implementing extended producer responsibility (EPR) regulations. The proposed model is easy to use, and the decision-makers can visualize the effects of their decisions on economic health of the organization to fulfil the growing needs of environmental conservation and social obligations by trading-off the number, location, and capacity of the recycling, refurbishing, collection, and disposal centers. The proposed model has been validated in a process industry (paint production). The results of the case organization suggest that integrating the refurbishing and recycling of the paint packaging is not only economically beneficial to the organization but is also environment friendly and helps to create jobs for low-skilled labor. Two novelties of the research work are the following: (i) the proposed model has been developed to handle carbon footprints generated in the recycling, refurbishing, and disposal processes as well as transportation, and (ii) the ε-constraint and LP-metric methods have been used to generate a set of Pareto-optimal solutions unlike single optimal solution. These Pareto-optimal solutions provide the flexibility to the organization to pick up optimal solutions with different environmental, social, and economic requirements to provide the government agencies data for EPR obligations.Item Optimization of Specific Energy, Scrap, and Surface Roughness in 3D Printing Using Integrated ANN-GA Approach(Elsevier, 2023) Kulshrestha, Rakhee; Sangwan, Kuldip Singh3D printing technology is fast emerging as a solution to convert cyber models to physical models quickly for visualization and feedback in Industry 4.0 environment. Energy efficiency, surface roughness, and material wastage are important performance responses and the effects of 3D printing parameters on these conflicting responses need to be studies to further improve the technology. Multiobjective optimization is a tool to obtain the right balance among conflicting performance responses. This paper aims to find the optimal values of infill, layer height, printing speed, extruder temperature, and scale to optimize specific energy, scrap, and surface roughness, simultaneously. Experiments were performed based on a Taguchi L-27 orthogonal array using PLA filament. A predictive model has been developed using artificial neural network (ANN) integrated with a genetic algorithm (GA) for obtaining Pareto solutions. Technique for order preference by similarity to ideal solution (TOPSIS) is used to obtain the most preferred solution from the Pareto solutions and analytical hierarchal process (AHP) is used to determine weights of the three objectives. The proposed methodology is expected to help the practitioners to rank and customise the decisions proactively in conflicting scenarios before the product is 3D printed, thereby improving sustainability and/or meeting product quality requirements